Counting points of bounded height in monoid orbits
Number Theory
2020-07-07 v2 Dynamical Systems
Abstract
Given a set of endomorphisms on , we establish an upper bound on the number of points of bounded height in the associated monoid orbits. Moreover, we give a more refined estimate with an associated lower bound when the monoid is free. Finally, we show that most sets of rational functions in one variable satisfy these more refined bounds.
Cite
@article{arxiv.2006.08563,
title = {Counting points of bounded height in monoid orbits},
author = {Wade Hindes},
journal= {arXiv preprint arXiv:2006.08563},
year = {2020}
}
Comments
Main result strengthened to generic sets of rational functions. An appendix by Umberto Zannier is included